In a distributed environment where multiple applications compete and share a limited amount of system resources, applications tend to suffer from variations in resource availability and are desired to adapt their behavior to the resource variations of the system. We propose a task control model to rigorously model the dynamics of an adaptive system using digital control theory. With our task control model, we are able to quantitatively analyze the stability and equilibrium of the adaptive applications, while simultaneously providing fairness guarantees to other applications in the system. Our control algorithm has also been extended to those cases where no sufficient task state information is observable. We show that even under these circumstances, our task control model can still be applied and our control algorithms yield stable and responsive behavior.